Derive Newton\'s law of gravitation from Kepler\'s third law of planet

1.	Derive Newton\'s law of gravitation from Kepler\'s third law of planetary motion
Answer» F=mv^2/rBut orbital vel isv=circumference/time=2πr/TBy putting value of v in first eqn we getF=m/r*(2πr/T)^2=4π^2mr/T^2Now by putting Kepler\'s law T^2=kr^3in above eqn we getF=4π^2mr/kr^3As the force b/w the sun and the planets is mutual,it should also be proportional to the mass M of the sun.4π^2/k is proportional to M so,4π^2/k=GMSo F=GMm/r^2

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